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Leighton Vaughan Williams, a professor at Nottingham Business School who specializes in betting research, has long held that betting markets are better predictors of election outcomes than polls. Yet ahead of the U.K. vote on whether to leave the European Union, the bookies failed as miserably as pollsters to predict the result — actually, they did much worse. At certain points on Thursday, the probability of a "remain" vote implied by betting odds stood at 90 percent.

When I asked Vaughan Williams what had happened, he gave a surprising answer for a believer in the wisdom of markets:

"The markets were expecting the undecideds to switch predominantly to the status quo, as this has happened in previous referendums, such as the Scottish referendum and the Quebec referendum; but in both those cases the mass papers were backing 'remain.'

"This time was different. It was The Sun and Daily Mail that won it and the impact these mass distribution tabloid papers have on the popular psyche, especially in whipping up emotion, is difficult to overestimate. It is another lesson learned," he said.

"One of the reasons it's gotten harder for experts — pollsters, bookmakers, economic modelers — to predict election outcomes is that too many people make up their minds too late. According to a recent report by the market research firm Opinium, 20 percent to 30 percent of voters make a final decision within a week of casting their ballots, half of them on the day of the vote. In the U.K., a lot of these last-minute deciders are swayed by the tabloid press."

The Sun has a perfect record of backing the winning side in every election and referendum in the U.K. has had. That could just mean it knows its audience well, but there's more to it than that.

In March, Aaron Reeves of Oxford University and two of his collaborators published a paper that studied the effect of the Sun's switches to the Labour Party in 1997 and back to the Conservatives in 2009-2010. "In both cases, the defections were led by the owner and are not primarily driven by changes in support for either party among the readers," Reeves wrote. "These defections create a unique quasi-natural experiment where Sun readers are exposed to changes that other groups are not."

The team found that the paper's moves added about 525,000 votes to the Labour tally in 1997 and about 550,000 to the Conservative one in 2010; these kinds of numbers could easily flip the result of the referendum, which "leave" won by fewer than 1.3 million votes.

In both cases, Reeves and his collaborators found, the underlying political beliefs of voters who switched did not change. That's important. The Sun's readership — about 14.4 million people a month — has a specific core demographic. According to YouGov, it's predominantly female, aged 40-54, concentrated in the Midlands, East Anglia and the Northeast of England, relies on television for news and agrees with statements like "This country is going to the dogs" and "An eye for an eye, a tooth for a tooth." The Sun doesn't try to change that profile or influence the basic beliefs of its core audience. Yet it can, and does, help people who hold these beliefs to make specific electoral choices.

Reeves and his collaborators formulated a "theory of naïve preferences," versus "enlightened preferences," to explain how it happens. "Persons who have naïve preferences have values grounded in issues other than ideologies or policy positions, typically involving perceived charisma or competence," they wrote. "Sun readers are less politically knowledgeable and have weaker commitments to particular ideologies and are therefore more likely to exhibit naïve preferences than other newspaper readers." These same readers could probably be persuaded to vote "remain."

"If the Sun had backed 'remain' yesterday, I am sure it would have prevailed," Vaughan Williams says.

Yet emotional appeals to their cautious conservatism — like the Thursday front page of another tabloid, the pro-remain Daily Mirror, featuring a black hole of uncertainty — apparently don't resonate with English voters the way that appeals to patriotism and love of country do.

The Sun's cover on Thursday said, "Independence Day. Britain's Resurgence" — a reference to the film sequel released in Britain on Friday; a mobilizing message if there ever was one.

During the Brexit campaign, the Sun has used the Queen's image twice to push for a "leave" vote: It was undeterred by a ruling by the U.K. media standards watchdog that its "Queen Backs Brexit" headline was inaccurate and misleading. That, too, is an example of emotional input into the voters' thinking. Even though Queen Elizabeth never publicly expressed support for Brexit, the paper formed an association between her image and the anti-EU cause in its readers' heads.

The tabloids' outsized role in swaying last-minute voters is, of course, only one theory to explain why professional predictors failed. Yet it is more convincing to me than the argument that rain and flooding deterred "soft remain" voters more than determined brexiters. All British voters are used to bad weather but despite the floods, London, Oxford and Cambridge voted overwhelmingly to stay in the European Union.

If the theory of the Sun's influence is correct, it has implications for the U.S. presidential election and other races in which charismatic populists take part and the debate is emotional. Polls and betting markets may not be capturing the last-minute impact of the media that people use to feed their confirmation biases. And in close votes, that impact may turn out to be decisive.